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The distribution |f|λ, oscillating integrals and principal value integrals

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Abstract

We study the coefficients of asymptotic expansions of oscillating integrals. We also consider the connection with the coefficients of Laurent expansions at candidate poles of the distribution |f|λ and show that some of these coefficients vanish. Next, we express some of the most important of these coefficients as the so-called principal value integrals, first introduced by Langlands. Together with our results on principal value integrals, this leads to new results on the vanishing of these coefficients.

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  1. Department of Mathematics, University of Leuven, Celestijnenlaan 200 B, B-3001, Leuven, Belgium

    Ph. Jacobs

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  1. Ph. Jacobs
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Jacobs, P. The distribution |f|λ, oscillating integrals and principal value integrals. J. Anal. Math. 81, 343–372 (2000). https://doi.org/10.1007/BF02788996

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  • DOI: https://doi.org/10.1007/BF02788996

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